1. R.2 Integer Exponents, Scientific Notation, and Order of Operations
Simplify expressions with integer exponents.
Solve problems using scientific notation.
Use the rules for order of operations.
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Integers as Exponents
When a positive integer is used as an exponent, it indicates the number of times a factor appears in a product.
For any positive integer n,
where a is the base and n is the exponent.
Example: 84 = 8 • 8 • 8 • 8
For any nonzero real number a and any integer m,
a0 = 1 and
Example: a) 80 = b)
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3. Properties of Exponents
Product rule
Quotient rule
Power rule
(am)n = amn
Raising a product to a power
(ab)m = ambm
Raising a quotient to a power
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Examples – Simplify.
a) r 2 • r 5
= r (2 + 5) = r 3 b)
c) (p6)4 = p ‒24 or
d) (3a3)4 = 34(a3)4
= 81a12 or e)
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Scientific Notation
Use scientific notation to name very large and very small positive numbers and to perform computations.
Scientific notation for a number is an expression of the type N  10m,
where 1  N < 10, N is in decimal notation, and m is an integer.
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Examples
Convert to scientific notation.
a) 17,432,000 =  107
b) = 2.4  1010
Convert to decimal notation.
a)  106 = 3,481,000
b)  105 =
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Another Example
Chesapeake Bay Bridge-Tunnel. The 17.6-mile-long tunnel was completed in Construction costs were $210 million. Find the average cost per mile.
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8. Rules for Order of Operations
Do all calculations within grouping symbols before operations outside. When nested grouping symbols are present, work from the inside out.
Evaluate all exponential expressions.
Do all multiplications and divisions in order from left to right.
Do all additions and subtractions in order from left to right.
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Examples
a) 4(9  6)3  18 = 4(3)3  18
= 4(27)  18
= 108  18
= 90 b)
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